Volume 103, Issue 5, Pages 907-917 (September 2012) Probing the Orientational Distribution of Dyes in Membranes through Multiphoton Microscopy  James E. Reeve, Alex D. Corbett, Igor Boczarow, Tony Wilson, Hagan Bayley, Harry L. Anderson  Biophysical Journal  Volume 103, Issue 5, Pages 907-917 (September 2012) DOI: 10.1016/j.bpj.2012.08.003 Copyright © 2012 Biophysical Society Terms and Conditions

Figure 1 (A) Transition dipole moment (TDM) of each molecule is tilted at an angle φ from the membrane normal and an angle ψ around it. The intensity of fluorescence or SHG from the ensemble of dyes is dependent on the angle away from the laser polarization, θ. (B) Variation of SHG from di-4-ANEPPS, which varies periodically with θ around the equator of a model membrane (giant unilamellar vesicle). The shape of this curve, when fit to a model, allows extraction of trigonometric moments of the tilt distribution, Ptilt(φ). The direction of laser excitation is co-linear with the direction of signal detection and perpendicular to the plane of the image in panel B. Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 2 Two different probability density functions can produce identical 〈φ〉 values (vertical line). Therefore, measures of 〈φ〉 alone do not adequately describe the system. For examples, these two probability density functions differ in where the lowest energy molecular tilt (μ) lies—i.e., normal to the membrane (solid) or tilted by 37° (shaded). Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 3 (A) Structure of di-4-ANEPPS and di-8-ANEPPS, the dyes used in this study and the membrane models used in this experiment: Phospholipid DPhPC (lipid) membranes incorporating ANEPPS dyes (solid and open lozenges) in (B) the water droplet model and (C) GUVs. Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 4 Flow chart for image processing with our polar fitting technique (left) and the oval profile technique (right), showing the reduction in the number of essential manual steps that may lead to error. Experimental steps (open), automatic steps (dark-shaded), and manual steps (light-shaded) result in the desired output (solid). (In each case, the dashed box represents the software used to process the image; steps outside of the dashed box require manual processing.) Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 5 Two-dimensional (A) angular function modeled with θ′ = π/2 (relative to polarization, double-headed arrow), ϑIPF = π/2, (B) radial function modeled with ρ′ = 100 pixels, σ = 10 pixels, ε = θ″ = 0 and (C) background function modeled with σ′ = 5 pixels and ε = θ″ = 0. Their combination results in Eqs. 10 and 11 that are represented by function (D). Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 6 Analysis of an SHG image of di-4-ANEPPS in a monolayer of DPhPC on the surface of a water droplet in oil. The polar-fitting technique renders the SHG image as a surface (A), with signal intensity plotted on the z axis and pixel location on the x and y axis. The parameterized model (B) is also plotted for comparison. Similarly, the two-dimensional SHG image (C) is plotted alongside the two-dimensional parameterized model (D) for comparison, image dimensions: 300 × 300 μm. We also include a plot from analysis of the image by the oval profile method (E). This method considers only a subset of data points (shaded points), which do not accurately represent the image and subsequently is prone to experience more error and a poorer fit (solid line). Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 7 One-photon fluorescence intensity around the equator of (A) a bleb on the exterior of a cultured HeLa cell stained with di-4-ANEPPS and (B) a model image of a single bleb reconstructed from the original image after parameterization, image dimensions: 26.5 × 26.5 μm. (C). This image was processed by using two methods. In the first, the oval profile method extracts data from the delineated area (dotted line) over the bleb. Each fitting technique generates an angular intensity fit that overlays the data (shaded points). The overlap of the signal data with background fluorescence from the cell can be seen as an anomaly on the polar plot from 345° to 60°. The polar fitting (solid line) is less influenced by this anomaly than the oval profile (dashed line), resulting in a better fit. Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 8 Two distinct tilt probability density functions (solid curves) showing φ (vertical solid line), and their contributing preferred tilt (dotted curves) and statistical (dot-dashed curve) terms. One PDF has a large μ and a small γ (B), whereas the other has a small μ and large γ (C). A representative cartoon (A) shows the physical interpretation of the quantities μ and γ, which may be calculated for given experimentally extracted order parameters. Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 9 Isosurface of the normalized linear combination of solutions to Eqs. 18, A–D, for di-4-ANEPPS in GUVs. The surface is plotted on a logarithmic scale in μ × γ space: (light shading) regions of lowest error. (Hatched area) Regions of very high root-mean-square error, which have been removed from the plot for clarity. (Solid disk) Solution presented in Table 1, found by a Levenberg-Marquardt minimization algorithm. The four contributing isosurfaces may be found in Fig. S10, Fig. S11, Fig. S12, and Fig. S13 in the Supporting Material. Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions

Figure 10 Probability density functions for di-4-ANEPPS (solid lines) and di-8-ANEPPS (dashed line) with accompanying expected tilt angles (vertical lines) for monolayers (solid) and GUVs (shaded). Biophysical Journal 2012 103, 907-917DOI: (10.1016/j.bpj.2012.08.003) Copyright © 2012 Biophysical Society Terms and Conditions